New exact explicit solutions of the generalized KdV equations

Senthilkumaran, M.; Pandiaraja, D.; Vaganan, B. Mayil

doi:10.1016/j.amc.2008.03.013

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Cited by 17 publications

(14 citation statements)

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“…Lot of studies have been conducted with this equation [1][2][3][4][5][6][7]. Some of them are the integrability aspects, soliton perturbation theory, quasi-stationarity, quasi-particle theory, stochasticity and many more.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of KdV equation with time-dependent coefficients

Johnpillai

Khalique

Biswas

2010

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Exact solutions of KdV equation with time-dependent coefficients

Johnpillai

Khalique

Biswas

2010

Applied Mathematics and Computation

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“…In 2008, this problem with the special case of n = 2 was solved using the Hirota's bilinear method [10]. Without any loss of generality it is assumed that the solitary wave solution to (1) is given by [1,4,5] q(…”

Section: Mathematical Analysismentioning

confidence: 99%

Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients

Biswas

2009

Nonlinear Dyn

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This paper obtains an exact solitary wave solution of the Korteweg-de Vries equation with power law nonlinearity with time-dependent coefficients of the nonlinear as well as the dispersion terms. In addition, there are time-dependent damping and dispersion terms. The solitary wave ansatz is used to carry out the analysis. It is only necessary for the timedependent coefficients to be Riemann integrable. As an example, the solution of the special case of cylindrical KdV equation falls out.

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“…There has been a lot of studies that has been carried out with this equation [1][2][3][4][5][6][7][8][9][10]. Some of the main aspects that has been studied in this equation are the integrability aspects, conservation laws, stochasticity issues, numerical simulation and many more.…”

Section: Introductionmentioning

confidence: 98%